Finely tunable dynamical coloration using bicontinuous micrometer-domains

Nanostructures similar to those found in the vividly blue wings of Morpho butterflies and colorful photonic crystals enable structural color through constructive interference of light waves. Different from commonly studied structure-colored materials using periodic structures to manipulate optical properties, we report a previously unrecognized approach to precisely control the structural color and light transmission via a novel photonic colloidal gel without long-range order. Nanoparticles in this gel form micrometer-sized bicontinuous domains driven by the microphase separation of binary solvents. This approach enables dynamic coloration with a precise wavelength selectivity over a broad range of wavelengths extended well beyond the visible light that is not achievable with traditional methods. The dynamic wavelength selectivity is thermally tunable, reversible, and the material fabrication is easily scalable.

The relative transmittance of SeedGel as a function of wavelength that covers UV-visible to the near-infrared range at different temperatures. The spectra are normalized to the spectrum of the liquid state sample measured at 20 ˚C. The relative transmittance is obtained by dividing the highest transmittance using the normalized spectra.

Modeling of Ultra-small angle neutron scattering (USANS) and small angle neutron scattering (SANS) data
Supplementary Fig 4 (a) shows the USANS scattering profiles of SeedGel measured at 27 ˚C, 28 ˚C, 29 ˚C, and 30 ˚C and their corresponding fittings using the Teubner-Strey model. The model has been widely used to describe bicontinuous structures and Sasview software was used to obtain the fitting results. [3][4][5][6] Teubner-Strey model (Eq-1 ~ Eq-4) is used to fit the scattering curve here. The parameters of periodicity (d), correlation length ( ), and the contrast between the two domains ((∆ ) 2 ) are allowed to vary, while other parameters are fixed as constants. is the volume fraction of one of the domains, which could be either the particle domain or the solvent domain. The volume fraction of the particle domain is determined from the ratio of the nominal particle concentration (about 24.3 %) over the local particle concentration in the particle domain. The local particle concentration in the particle domain is obtained from the fitting of SANS data at the highq region, which is discussed in the next paragraph. Based on the fitting results listed in Supplementary Tab 1, the periodicity of SeedGel at 30 ˚C is about 3.4 μm. Consistent with the unchanged peak position in the temperature range between 27 ˚C and 30 ˚C, the periodicity of the bicontinuous domains of around 3.4 μm is observed within the temperature range that SeedGel exhibits dynamically tunable optical properties. The slight intensity change at varied temperatures is due to the solvent exchange between domains, which affects the contrast between the bicontinuous domains.
(1− )(∆ ) 2 2 / 2 + 1 2 + 2 4 Eq-1 To obtain the local particle concentration in the particle domain, the SANS results are fitted using sphere model with the Hayter-Penfold method at different temperatures ( Supplementary Fig 4(b)). 7,8 Static decoupling approximation (β-approximation) is used to account for the polydispersity of the nanoparticles. 9 The radius of the nanoparticles is assumed to follow Gaussian distribution. Its polydispersity is defined as the standard deviation over the mean of the distribution, which is fixed at 0.1. The scattering length density of the solvent, volume fraction of particles in the particle domain, and the charge on the particle surface are left as variables of the fitting. All the rest of the parameters are fixed as constants. The radius of the sphere is determined by an independent experiment on a dilute sample with 0.5 % volume fraction silica nanoparticles dispersed in water. 1 The radius used in the fitting is 13.3 nm. The volume fractions of the particles in the particle domain at different temperatures are summarized in Supplementary Tab 1. It is clear that the local volume fractions of the particles in the particle domain stay around 40 % for all four temperatures, which is much higher than the particle concentration in the liquid dispersion state ( about 24 %).

Small angle X-ray scattering (SAXS) measurements rule out the formation of colloidal crystals.
Photonic crystals are known to scatter light at a certain wavelength that is related to their lattice parameter. Typically, they have ordered structures with an inter-particle distance of a few hundred nanometers (comparable to the wavelength of light) so that the materials can preferentially reflect light at a certain wavelength.
Ultra-small angle X-ray scattering (USAXS) and small angle X-ray scattering (SAXS) are used to investigate the structures of particles in the SeedGel sample at different temperatures (Supplementary Fig 5). Due to the large contrast between the silica particles and solvent, the SAXS scattering pattern, I(q), is mainly sensitive to particle structures. Here, q is the scattering wave vector with q = (4π/λ) sin(θ/2), where λ is the wavelength of X-ray and θ is the scattering angle. The inter-particle distance estimated from the inter-particle structure factor peak is about 30 nm close to the diameter of the silica nanoparticles. There are no sharp peaks that are typically observed for crystalline samples. Thus, the silica nanoparticles are packed in a disordered state without any long-range periodic structure. The results are consistent with the SANS data in Figure  2

Estimation of the averaged refractive index as the function of the wavelength for both the particle and solvent domains.
To calculate the averaged refractive index of both the particle and solve domains, the composition of each domain needs to be estimated first.
Our SAXS experiments show that the inter-particle peak intensity at ~ 0.02 Å -1 remains the same in the gel state. Thus, the particle packing is not affected by the solvent composition change in the particle domain as the SAXS is sensitive to the particle structures, but it is less sensitive to the solvent composition change.
To obtain the solvent composition in each domain, we perform a SANS experiment as it can be sensitive to the solvent composition. To achieve this, we adjust the scattering length density (SLD) of water to be the same as that of silica with the volume ratio between H2O and D2O to be 42: 58. When there is a 2,6-lutidine exchange between particle domain and solvent domain, the scattering contrast (SLD difference) between silica particle and the surrounding solvent is altered. By analyzing the contrast change, the solvent composition in the particle domain can be estimated. Based on the mass balance, we can further estimate the composition in the solvent domain.
The SANS results are presented in Supplementary Fig 6. In the gel state, the scattering intensity at > 0.02 Å -1 is mainly due to the difference of SLD between silica and the solvent around the particles in the particle domain. The SLD of the silica particles remains the same at all probed temperatures. However, the SLD of the solvent surrounding the particles is affected by the solvent composition. In the liquid state, the SLD of the solvent is a mixture of lutidine and water. In the gel state, the lutidine concentration is reduced in the solvent of the particle domain. The SLD difference between silica particles and the surrounding solvent becomes much smaller as the SLD of water is matched to that of silica. Therefore, the scattering intensity of the inter-particle peak at ~0.02 Å -1 is greatly reduced in the gel state compared to that in the liquid state (20 ˚C). 1 Ramping up the temperature further decreases the lutidine concentration and increases the water concentration in the particle domain. Using a method discussed previously, 1 it is calculated that the mass fraction of lutidine could decrease from 15.3 % to 9.7 % in the particle domain when the temperature is increased from 27.5 ˚C to 30 ˚C. The lutidine concentration in the solvent domain can be estimated based on the mass balance. The amounts of different components in both domains are listed in Supplementary Tab 2. It is important to note that the fraction of each component is normalized to the total mass of solvent in each domain. In the calculation, the concentration of silica nanoparticles in the particle domain is fixed at a volume fraction of 39.1 % based on the SAXS results.
Supplementary Tab 2. The calculated mass fraction of lutidine and water in both particle and water domain. With the estimated solvent composition of each component in both domains, the refractive index can be estimated using the Lorentz-Lorenz formula (Eq-5). The mass density (ρ), Avogadro's number (N), molecular polarity (θ), and molecular weight (M) are used to obtain the refractive index (n). In this equation, F is a corrective term related to the mixing of lutidine and water close to its critical temperature. The refractive index of the binary solvent within this temperature range has been investigated and documented in the literature. 10 The mixture of water and lutidine shows a strong wavelength (λ) and temperature (T) dependence, which is described in Eq-6. 10 In Eq-6, is the mass fraction of lutidine, whereas T0 is 33.5 ˚C and λ0 is 632. The refractive index of the particle domain can be obtained with a knowledge of the refractive index of the binary solvent and silica particles using the Lorentz-Lorenz formula (Eq-8). It is reasonable to assume that the refractive index of silica is independent of temperature change between 26 ˚C and 30 ˚C. The refractive indices of both the particle domain and solvent domain depend on temperature because the solvent exchanges between domains result in a change of solvent composition. In the calculation, the binary solvent is treated as one component and silica nanoparticles are treated as a second component. Their molecular polarities are calculated from their corresponding refractive indices using Eq-8. The mixing rule described in Eq-9 is used to determine the averaged molecular polarity when silica particles are mixed with the binary solvent, where c is the mole fraction of one of the components.
It is worth mentioning that the absolute value of the refractive index of silica strongly depends on its polymorph. 11,12 Fused silica and quartz have different values of refractive index, which are plotted as a function of wavelength in Supplementary Fig 7(a). (The difference is about 0.086 over the studied wavelength range.) However, it is important to point out that the two polymorphs exhibit similar wavelength dependence. By vertically shifting the refractive index of fused silica by 0.086, the curve of fused silica almost overlaps with that of quartz.
The refractive index of the particle domain in our SeedGel is calculated using both polymorphs of silica. The results are shown in Supplementary Fig 7(b). There is no observable discrepancy after shifting the refractive index of one curve by 0.034 as shown in Supplementary Fig 7(b). The polymorph of the silica does not affect the wavelength dependence of the refractive index of the particle domain. Therefore, the type of silica we use to estimate the refractive index does not affect the curvature of the curve. Hence, we used the refractive index of fused silica for the rest of the calculations. 12 The dynamical tunability of optical transmission of the SeedGel is mainly driven by the different wavelength dependence of the refractive index between the particle domain and solvent domain. The volume fraction of silica particles in the particle domain is 39.1 %. For the binary solvent in the particle domain, the mass concentration of lutidine and water is 15.3 %, 84.7 % respectively. These particle and solvent concentrations correspond to the compositions of the particle domain at 27.5 ˚C.
As the values of the refractive index of the binary solvent have been well studied in literature 10 , the final value of the refractive index of the particle domain is calibrated by vertically shifting the calculated value to match that of the solvent domain at the wavelength of the transmittance peak. This is because when the refractive indices of the two domains are the same, the transmittance should reach the maximum value as the scattering intensity is minimized due to the lack of the scattering contrast. The refractive index of the particle domains in Supplementary Fig 8(a) is shifted vertically by 0.0229. This is based on the experimental fact that the sample is transparent for light with short wavelengths at low temperatures. The obtained refractive indices of the particle domain and the solvent domain as a function of wavelength are shown in Supplementary Fig 8(a) and Supplementary Fig 8(b), respectively.
Importantly, the wavelength dependence (curvature) of the two domains is different. When increasing temperature, the refractive index of the particle domain decreases, and that of the solvent domain increases. Due to the different wavelength dependence of the refractive index, the matching wavelength, where the refractive indices of both domains are identical, shifts from a shorter wavelength to a long wavelength. This is further discussed in detail in Section 7 of the supporting information. By changing temperature from 30 ˚C to 27.5 ˚C, the combined change in the refractive index of these two domains is approximately 0.0135. 6. Static light scattering measurement also confirms the wavelength-dependent refractive index matching between the particle and the solvent domains.
The static light scattering (SLS) measurements were performed with a modified Brookhaven BI-200SM using a wavelength of 532 nm laser light from a Coherent VERDI diode-pumped solidstate laser operating in TEM00 mode. Glan-laser polarizer and analyzer (Thorlabs) were used under the vertical polarizer and vertical analyzer conditions. The laser power was finely adjusted by neutral density filters, and a 1-mm pinhole was used before the photomultiplier. The scattered intensity I(q) was collected between the scattering angles of 20° to 140° in 5° increments enabled by the precision goniometer and detector arm, corrected for reflection, angle-dependent scattering volume variation, and refraction by standard methods, and subsequently plotted as a function of scattering wave vector q, where q = (4πn/λ) sin(θ/2). Here, n is the refractive index. All samples were thermostatically controlled by a recirculating bath to control the temperature of the decalin index matching bath. The sample temperature was monitored by a platinum resistance thermocouple placed within the vat, with a precision of ± 0.1 °C. Supplementary Fig 9. Static light scattering results of SeedGel performed at different temperatures with a 532 nm laser. The error bars in the figure represent one standard deviation and are often smaller than the symbol size.
The SLS results of a SeedGel sample are shown in Supplementary Fig 9. Note that the wavelength of the laser is 532 nm. The flat scattering curves of the solvent mixture (lutidine and water) at different temperatures indicate that the solvent mixture itself does not form structures at the length scale corresponding to the q-range probed by the SLS. In contrast, the SeedGel sample exhibits a large scattering intensity at 27 ˚C. Further increasing the temperature reduces the scattering intensity. The scattering pattern shows the lowest intensity at 28.1 ˚C. At 28.6 ˚C, the scattering intensity increases again. This is consistent with the proposed mechanism in the previous section.
The strong scattering at 27 ˚C is due to the mismatch of the refractive index of the two domains at this particular wavelength. Further increasing the temperature shifts the matching wavelength closer to the used laser wavelength and reduces the contrast between the two domains. The lowest static light scattering intensity occurs at 28.1 ˚C where the matching point of the wavelength of these two domains is very close to the laser wavelength. Further increasing the temperature shifts the matching wavelength and increases the contrast at the wavelength of the laser resulting in increased scattering intensity at 28.6 ˚C.
This trend measured by the light scattering experiment is consistent with the transmission results in Figure 1 in the main text. By increasing the temperature from 27 ˚C, the transmission of 532 nm light gradually increases, indicating a reduced contrast between domains. It results in a decrease of the static scattering intensity from 27 ˚C to 28.1 ˚C. The transmittance of 532 nm light reaches a maximum close to 28.1 ˚C, suggesting a matched refractive index between the domains.

Calculation of light transmittance of a SeedGel sample
It is well known that the transmitted intensity of light (I) can be related to the incoming intensity (I0) by 0 = − , where Σ is the macroscopic scattering cross section and d is the sample path length. For a general case, Σ depends on both the scattering and absorption cross section. Since the temperature effect of the light absorption is negligible within the studied temperature range, the temperature-dependent transmittance in our SeedGel samples is thus solely due to the change of the scattering cross section. And the macroscopic scattering cross section is proportional to the contrast, (Δρ) 2 , where Δρ is the refractive index difference between two domains.
Thus the light transmittance can be described by Eq-10. Here, Δρ can be estimated using Eq-11, which is closely related to the refractive indices of the particle domain (np) and solvent domain (ns). 13 Here, λ in Eq-11 is the wavelength of light. 'A' is related to the structure of the SeedGel during the studied temperature range. As the bicontinuous domain structures remain the same during the experiment, 'A' can be considered as a constant value with the investigated temperature range. Here, a fixed value of 6.54 × 10 10 Å 3 is chosen for 'A' as it results in a very good agreement of the estimated transmittance with the experimental results during the investigated temperature range. Note that for all calculated transmittance at different temperatures, 'A' is a fixed constant. Eq-11 Increasing the temperature decreases and increases . Because the wavelength dependence of the two domains is different from each other, the refractive index between the two domains only matches at a single wavelength at a given temperature. Heating the SeedGel sample results in a shift of the matching point towards the longer wavelength. As a result, the position of the transmittance peak shifts to a longer wavelength when increasing the temperature.
The theoretically calculated transmission spectra together with the estimated refractive index of the two domains are shown in the same figure (Supplementary Fig 10). The results in panels (a) to (h) correspond to the sample from the low temperature ( Supplementary Fig 10 (a)) to the high temperature ( Supplementary Fig 10(h)). The refractive index of the solvent domain plotted in Supplementary Fig 10 (a) is based on the estimated results of SeedGel at 27.5 ˚C. Since the effect of the temperature change is only to slightly shift the whole wavelength-dependent refractive index curve in the vertical direction, only the refractive index of the particle domain is adjusted from Supplementary Fig 10 (a) to Supplementary Fig 10 (h) to simplify the calculation. This is reasonable as only the refractive index difference between the two domains matters when estimating the light transmission.
The peak transmittance (100 %) occurs at the wavelength that the refractive index of the two domains match. Light at other wavelengths is scattered away by the sample since the large domain size of the SeedGel scatters strongly even with a very minor difference of the refractive index. Based on the estimation, the relative difference of the refractive index between the two domains only needs to change by 0.007 to shift the transmission peak across the whole visible spectrum. Based on the actual composition of each component estimated from SANS measurements in both domains ( Supplementary Fig 6), the total change of refractive index difference can be as large as 0.0135 when the temperature changes from 27.5 ˚C to 30 ˚C ( Supplementary Fig 8 in the Supporting Information). This large change of the refractive index also allows the SeedGel to finely control the peak position of the light transmittance in the ultraviolet and infrared region.